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arXiv · 1410.6199

The strong Kervaire invariant problem in dimension 62

Zhouli Xu
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Abstract

Using a Toda bracket computation $\langle θ_4, 2, σ^2\rangle$ due to Daniel C. Isaksen [11], we investigate the $45$-stem more thoroughly. We prove that $θ_4^2=0$ using a $4$-fold Toda bracket. By [2], this implies that $θ_5$ exists and there exists a $θ_5$ such that $2θ_5=0$. Based on $θ_4^2=0$, we simplify significantly the $9$-cell complex construction in [1] to a $4$-cell complex, which leads to another proof that $θ_5$ exists.

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Zhouli Xu. 2014-10-22. The strong Kervaire invariant problem in dimension 62. https://doi.org/10.2140/gt.2016.20.1611

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